Solve the problemintegral of y=x^3/(x^4+1)^5

Given y= x^3/ (x^4 +10^5

We
need to find the integral of y.

==> intg y = intg (
x^3/(x^4 +1)^5

Let us assume that u = x^4 + 1   ==>
du = 4x^3 dx

Now we will
substitute.

==> intg y = intg ( x^3 / u^5) * du/
4x^3

We will reduce similar
terms.

==> intg y = intg ( du/ 4u^5
)

= (1/4) intg u^-5 du

= (1/4)
u^-4 / -4  + C

= (-1/16) u^-4 +
C

= -1/16u^4 + C

Now we will
substitute with u = x^4 +1

==> intg y
= (-1/16)*(x^4+1)^4 + C